Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

What is the angle (in circular measure) between the hour hand and the minute hand of a clock when the time is half past $4$?

  1. $\dfrac{\pi}{3}$
  2. $\dfrac{\pi}{4}$
  3. $\dfrac{\pi}{6}$

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In the clock the angle between each hour division will be $\dfrac { 360 }{ 12 } =30^{o}$. 

Now here at $4:30$, the hour hand will be along AB which is the angle bisector between $4$ and $5$ and the minute hand will be along AC,
The angle between them will be $=30+15=45$,in radians $\dfrac { \pi  }{ 4 }$ 

Hence, B is correct.

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

At what time is the angle between the hands of a clock equal to $30^{o}$ ?

  1. $1:00$
  2. $11:00$
  3. $2:00$
  4. $12:00$
Reveal answer Fill a bubble to check yourself
A,B Correct answer
Explanation

A clock is a circle made of $360^\circ$, and that each hour represents an angle and the separation between them is $\dfrac{360^\circ}{12}=30^\circ$


Hence, 
At $1:00$ the angle between the hands is $30^\circ$, minute hand pointing at 12 and hour hand at 1.

Similarly
At $11:00$ the angle between the hands is $30^\circ$

At $2:00$ the angle between the hands is $60^\circ$

At $12:00$ the angle between the hands is $0^\circ$

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

How many times between $6:00$ am and $6:00$ pm, do the hands of a clock make a straight line 

  1. $9$
  2. $10$
  3. $11$
  4. $12$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours.

 (Because between 5 and 7 they point in opposite directions at 6 o'clock only).

So between $6:00$ am to $6:00$ pm ($12$ hours), $11$ times hands of a clock make a straight line.
Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

How many times in a day, do the hands of a clock make a right angle ?

  1. $21$
  2. $22$
  3. $42$
  4. $44$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

There will be $2$ times per hour when the angle between minute and hour hand is $90^\circ$

Total of $22$ times in $12$ hours.
$\therefore$ In $24$ hours, $22\times 2=44$ times the angle between minute and hour hand is $90^\circ$.

Multiple choice maths construction of angles angles in a clock checking angles between hands of a clock clock with respect to angles measuring and drawing angles

At 2:15 o'clock, the hour and minute hands of a clock form an angle of:

  1. $30^{\circ}$
  2. $5^{\circ}$
  3. $22\dfrac{1}{2}{\circ}$
  4. $7\dfrac{1}{2}{\circ}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
   $\underset { \downarrow  }{ \underline { 2 }  } <2:15<\underset { \downarrow  }{ 3 } $' $O$ clock
$\left( { 60 }^{ 0 } \right) $             $\left( { 90 }^{ 0 } \right) $
when minute hand rotates $15$ min hour hand rotate $\dfrac { 15 }{ 60 } \times { 30 }^{ 0 }={ 7.5 }^{ 0 }$
So, angle at $2:15$ is $=\left( { 90 }^{ 0 }-\left( { 60 }^{ 0 }+{ 7.5 }^{ 0 } \right)  \right) ={ 22.5 }^{ 0 }$
Multiple choice maths complex numbers and linear inequations argand plane and polar representation geometric representation of a complex number complex numbers and quadratic equations

A particle starts from a point $z _0= I + i$, where $i
=\sqrt{-1}$ It moves horizontally away from origin by $2$ units and then
vertically away from origin by $3$ units to reach a point$ z _1$. From $z _1$
particle moves $\sqrt{5}$ units in the direction of $2\hat i + \hat j$ and
then it moves through an angle of $\cos e{c^{ - 1}}\sqrt 2 $ in anticlockwise
direction of a circle with centre at origin to reach a point $z _2$ . The arg $z _2$ is given by

  1. ${\sec ^{ - 1}}2$
  2. ${\cot ^{ - 1}}0$
  3. ${\sin ^{ - 1}}\left( {\dfrac{{\sqrt 3 - 1}}{{2\sqrt 2 }}} \right)$
  4. ${\cos ^{ - 1}}\left( {\dfrac{{ - 1}}{2}} \right)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The problem involves complex number transformations. Given the starting point and movements, the final argument calculation leads to an angle of 90 degrees, which corresponds to cot inverse of 0.

Multiple choice maths complex numbers and linear inequations argand plane and polar representation geometric representation of a complex number complex numbers and quadratic equations

The number of solution of $z^2 + \bar{z} = 0$ is

  1. $5$
  2. $4$
  3. $2$
  4. $3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Let $z=x+iy$.
Now,
$z^2+\overline{z}=0$
or, $x^2-y^2+2ixy+(x-iy)=0$
or, $(x^2-y^2+x)+i(2xy-y)=0$
Now comparing the real and imaginary part both sides we get,
$x^2-y^2+x=0$.....(1) and $2xy-y=0$.....(2).
From (2) we get, $x=\dfrac{1}{2}$ or $y=0$.
Now $x=\dfrac{1}{2}$ gives from (1) we get, $y=\pm \dfrac{\sqrt{3}}{2}$.
And $y=0$ gives from (1) we get, $x=0, 1$.
So the solution s are $(0,0), (1,0), \left(\dfrac{1}{2},\pm \dfrac{\sqrt{3}}{2}\right)$.
So we have $4$ solutions.
Multiple choice maths complex numbers and linear inequations argand plane and polar representation geometric representation of a complex number complex numbers and quadratic equations

If $z \neq 0$, then $ \overset{100}{\underset{0}{\int}}arg(-|z|)dx =$

  1. $0$

  2. Not defined
  3. $100$
  4. $100\pi$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For any non-zero complex number z, -|z| is a negative real number. The argument of any negative real number is pi. Therefore, arg(-|z|) = pi. Integrating this constant function with respect to x from 0 to 100 gives the integral of pi dx from 0 to 100, which evaluates to pi * (100 - 0) = 100pi.

Multiple choice maths complex numbers and linear inequations argand plane and polar representation geometric representation of a complex number complex numbers and quadratic equations

The complex no. $\dfrac{1+2i}{1-i}$ lies in which quadrant of the complex plane

  1. first

  2. second

  3. third

  4. fourth
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find the quadrant, multiply the numerator and denominator by the conjugate (1+i). (1+2i)(1+i) / (1-i)(1+i) = (1+i+2i-2) / 2 = (-1+3i) / 2 = -0.5 + 1.5i. This point lies in the second quadrant.